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%I #27 Sep 08 2022 08:45:05
%S 1,7,10,31,22,37,25,19,16,34,4,28,1,7,10,31,22,37,25,19,16,34,4,28,1,
%T 7,10,31,22,37,25,19,16,34,4,28,1,7,10,31,22,37,25,19,16,34,4,28,1,7,
%U 10,31,22,37,25,19,16,34,4,28,1,7,10,31,22,37,25,19,16,34,4,28,1,7,10,31
%N a(n) = 7^n mod 39.
%H G. C. Greubel, <a href="/A070422/b070422.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1,0,1,0,-1,0,1).
%F From _R. J. Mathar_, Apr 20 2010: (Start)
%F a(n) = a(n-2) - a(n-4) + a(n-6) - a(n-8) + a(n-10).
%F G.f.: ( -1-7*x-9*x^2-24*x^3-13*x^4-13*x^5-12*x^6-6*x^7-4*x^8-28*x^9 ) / ( (x-1)*(1+x)*(1+x+x^2)*(x^2-x+1)*(1-x^2+x^4) ). (End)
%F a(n) = a(n-12). - _G. C. Greubel_, Mar 22 2016
%t PowerMod[7, Range[0, 50], 39] (* _G. C. Greubel_, Mar 22 2016 *)
%o (Sage) [power_mod(7,n,39) for n in range(0,76)] # _Zerinvary Lajos_, Nov 27 2009
%o (PARI) a(n)=lift(Mod(7,39)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o (Magma) [Modexp(7, n, 39): n in [0..100]]; // _Bruno Berselli_, Mar 22 2016
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
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